q‐regular variation and the existence of solutions of half‐linear q‐difference equation
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DOI: 10.1002/mma.7570
Abstract: The half‐linear q‐difference equation Dq(p(t)Φ(Dq(x(t))))+r(t)Φ(x(qt))=0,t∈qℕ0={qn:n∈ℕ0},q>1, where Φ(x)=|x|αsgnx , α>0,p:qℕ0→(0,∞),r:qℕ0→ℝ , is analyzed in the framework of q‐regular variation. Necessary and sufficient conditions for the existence of q‐regularly varying solutions are given, under the assumption that… read more here.
Keywords: regular variation; half linear; linear difference; difference equation ... See more keywords
On Ulam stability of a third order linear difference equation in Banach spaces
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DOI: 10.1007/s00010-020-00722-5
Abstract: We obtain a result on Ulam stability and on the best Ulam constant for the linear difference equation $$x_{n+3}=ax_{n+2}+bx_{n+1}+c x_n,$$$$a,b,c \in \mathbb {K}$$, where $$\mathbb {K}$$ is one of the fields $$\mathbb {R}$$ or $$\mathbb… read more here.
Keywords: difference equation; linear difference; ulam stability;
Modelling and simulation of deformation behaviour during drying using a concept of linear difference method
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DOI: 10.1007/s00226-017-0897-6
Abstract: This study deals with the development of a two-dimensional model to simulate the deformations in wood samples during the wood drying process for the evaluation of the drying quality. The samples cut from sapwood of… read more here.
Keywords: simulation deformation; deformation; linear difference; simulation ... See more keywords
On the best Ulam constant of a first order linear difference equation in Banach spaces
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DOI: 10.1007/s10474-020-01098-3
Abstract: We obtain some results on Ulam stability for the linear difference equation $$x_{n+1}=a_nx_n+b_n,\, n\geq0$$ , in a Banach space X. If there exists $$\lim_{n\to\infty}|a_n|=\lambda$$ , then the equation is Ulam stable if and only if… read more here.
Keywords: linear difference; best ulam; difference equation; equation ... See more keywords
Galois groups for integrable and projectively integrable linear difference equations
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DOI: 10.1016/j.jalgebra.2017.02.032
Abstract: We consider first-order linear difference systems over C(x)C(x), with respect to a difference operator σ that is either a shift σ:x↦x+1σ:x↦x+1, q -dilation σ:x↦qxσ:x↦qx with q∈C×q∈C× not a root of unity, or Mahler operator σ:x↦xqσ:x↦xq… read more here.
Keywords: groups integrable; difference; integrable projectively; galois groups ... See more keywords
Oscillation and non-oscillation criteria for linear and half-linear difference equations
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DOI: 10.1016/j.jmaa.2017.03.012
Abstract: Abstract We find very general classes of linear and half-linear difference equations which are conditionally oscillatory. We identify the critical oscillation constant whose value implies the oscillation or non-oscillation of studied equations. Our results are… read more here.
Keywords: difference equations; oscillation non; oscillation; linear half ... See more keywords
Second order linear difference equations
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DOI: 10.1080/10236198.2017.1408608
Abstract: Abstract We provide the explicit solution of a general second order linear difference equation via the computation of its associated Green function. This Green function is completely characterized and we obtain a closed expression for… read more here.
Keywords: order linear; difference equations; difference; second order ... See more keywords
Asymptotic summation of perturbed linear difference systems in critical case
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DOI: 10.1080/10236198.2019.1662412
Abstract: We propose an asymptotic summation method for certain class of linear difference systems. Both the ideas of the centre manifold theory and the averaging method are used to construct the asymptotics for solutions. We illustrate… read more here.
Keywords: summation perturbed; difference; asymptotic summation; difference systems ... See more keywords
Approximation of experimental data by solving linear difference equations with constant coefficients (in particular, by exponentials and exponential cosines)
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DOI: 10.1134/s1054661817020109
Abstract: This paper proposes a method for approximating experimental data points by the curves representing the solutions of linear difference equations with constant coefficients, in particular, by the curves of the expcos class. An algorithm for… read more here.
Keywords: difference equations; constant coefficients; coefficients particular; experimental data ... See more keywords
Oscillation of a second order half-linear difference equation and the discrete Hardy inequality
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DOI: 10.14232/ejqtde.2017.1.43
Abstract: In local terms on finite and infinite intervals we obtain necessary and sufficient conditions for the conjugacy and disconjugacy of the following second order half-linear difference equation ∆(ρi|∆yi|∆yi) + vi|yi+1|yi+1 = 0, i = 0,… read more here.
Keywords: order half; second order; linear difference; half linear ... See more keywords
Hautus–Yamamoto criteria for approximate and exact controllability of linear difference delay equations
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DOI: 10.3934/dcds.2023049
Abstract: The paper deals with the controllability of finite-dimensional linear difference delay equations, i.e., dynamics for which the state at a given time $t$ is obtained as a linear combination of the control evaluated at time… read more here.
Keywords: exact controllability; linear difference; delay equations; difference delay ... See more keywords